The masses, yyy grams, of 15 dragon fruits randomly sampled from a large harvest were measured and recorded. The following summary statistics were obtained:
∑y=6750,∑y2=3042450 \sum y = 6750, \quad \sum y^2 = 3042450 ∑y=6750,∑y2=3042450Calculate unbiased estimates of the mean and the variance of the masses of the dragon fruits in the harvest.
Agricultural research suggests that the masses of these dragon fruits follow a normal distribution with a standard deviation of 18 g.
Calculate a 95% confidence interval for the mean mass of dragon fruits in the harvest. Give the limits of your confidence interval to 2 decimal places.
The farm manager claims that the results in part (b) indicate that it is highly unlikely for a fruit to weigh less than 420 g.
Use your answer to part (b) to estimate the smallest proportion of dragon fruits in the harvest that are expected to have a mass less than 420 g.
